Question: Find the greatest common factor of $80$ and $20$.
Solution: The greatest common factor (GCF) is the largest number that is a factor of both $80$ and $20$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}80 &=2\cdot2\cdot2\cdot2\cdot5\\\\\\\\ 20&=2\cdot2\cdot5 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}80 &=2\cdot2\cdot2\cdot2\cdot5\\\\\\\\ 20&=2\cdot2\cdot5 \end{aligned}$ Each number shares the factors ${2}, {2},$ and $5,$ so the GCF is $2\cdot2\cdot5={20}$. The greatest common factor of $80$ and $20$ is $20$.